To find the equation of a line that passes through the point [tex]\((3, 2)\)[/tex] and is parallel to the line [tex]\(y = 3x - 4\)[/tex], we can follow these steps:
### Step 1: Identify the Slope
First, we need to know that lines that are parallel have the same slope. The given line has the equation [tex]\(y = 3x - 4\)[/tex], and the slope (denoted as [tex]\(m\)[/tex]) of this line is the coefficient of [tex]\(x\)[/tex], which is [tex]\(3\)[/tex].
### Step 2: Use the Point-Slope Form
Next, we use the point-slope form of the equation of a line, which is given by:
[tex]\[y - y_1 = m(x - x_1)\][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] is the given point [tex]\((3, 2)\)[/tex] and [tex]\(m\)[/tex] is the slope [tex]\(3\)[/tex].
Plugging in the values, we get:
[tex]\[y - 2 = 3(x - 3)\][/tex]
### Step 3: Solve for [tex]\(y\)[/tex]
To find the equation in slope-intercept form ([tex]\(y = mx + b\)[/tex]), we solve for [tex]\(y\)[/tex]:
[tex]\[y - 2 = 3(x - 3)\][/tex]
[tex]\[y - 2 = 3x - 9\][/tex]
[tex]\[y = 3x - 9 + 2\][/tex]
[tex]\[y = 3x - 7\][/tex]
### Conclusion
Thus, the equation of the line that passes through the point [tex]\((3, 2)\)[/tex] and is parallel to the line [tex]\(y = 3x - 4\)[/tex] is:
[tex]\[ \boxed{y = 3x - 7} \][/tex]
